Classification Of N+2-Dimensional N-Lie Algebras

An n-Lie algebra is a natural generalization of the concept of a Lie algebra to the case, where the fundamental multiplication is n-ary. (n≥2. when n= 2. the definition agrees with the usual definition of a Lie algebra). In this thesis, we mainly study the classification of (n+2)-dimensional n-Lie algebras.In section 1, we recall some definitions, notations and some basic results for n-Lie algebras, such as definitions of n-Lie algebra. subalgcbras. derivation algebras. ideals, solvability. nilpotent. centers and Toral subalgebras.In section 2, we refine the classification of (n+1)-dimensional n-Lie algebras over an algebraically closed field of characteristic zero.In section 3. we study the basic structure of (n+2)-dimensional n-Lie algebras over an algebraically closed field of characteristic zero.In section 4. we discuss the classification of (n+2)-dimensional n-Lie algebras over an algebraically closed field of characteristic zero. and we also prove the isomorphic criterion theorem of (n-2)-dimensional n-Lie algebras.